Descriptions of state spaces of orthomodular lattices (the hypergraph approach)
Mathematica Bohemica (1992)
- Volume: 117, Issue: 3, page 305-313
- ISSN: 0862-7959
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topNavara, Mirko. "Descriptions of state spaces of orthomodular lattices (the hypergraph approach)." Mathematica Bohemica 117.3 (1992): 305-313. <http://eudml.org/doc/29434>.
@article{Navara1992,
abstract = {Using the general hypergraph technique developed in [7], we first give a much simpler proof of Shultz's theorem [10]: Each compact convex set is affinely homeomorphic to the state space of an orthomodular lattice. We also present partial solutions to open questions formulated in [10] - we show that not every compact convex set has to be a state space of a unital orthomodular lattice and that for unital orthomodular lattices the state space characterization can be obtained in the context of unital hypergraphs.},
author = {Navara, Mirko},
journal = {Mathematica Bohemica},
keywords = {affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation; orthomodular lattice; state space; affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation},
language = {eng},
number = {3},
pages = {305-313},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Descriptions of state spaces of orthomodular lattices (the hypergraph approach)},
url = {http://eudml.org/doc/29434},
volume = {117},
year = {1992},
}
TY - JOUR
AU - Navara, Mirko
TI - Descriptions of state spaces of orthomodular lattices (the hypergraph approach)
JO - Mathematica Bohemica
PY - 1992
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 117
IS - 3
SP - 305
EP - 313
AB - Using the general hypergraph technique developed in [7], we first give a much simpler proof of Shultz's theorem [10]: Each compact convex set is affinely homeomorphic to the state space of an orthomodular lattice. We also present partial solutions to open questions formulated in [10] - we show that not every compact convex set has to be a state space of a unital orthomodular lattice and that for unital orthomodular lattices the state space characterization can be obtained in the context of unital hypergraphs.
LA - eng
KW - affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation; orthomodular lattice; state space; affine homeomorphism; compact convex set; hypergraph; unital orthomodular lattices; state space representation
UR - http://eudml.org/doc/29434
ER -
References
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